HOUSTON — Raising campaign cash in Republican territory, President Barack Obama on Friday hailed a rebounding economy and accused Republicans of banking on voters having “amnesia” about the steps that led to a brutal economic collapse.

Bidding for re-election, Obama bounded between a rally-style event in a sprawling Rolls-Royce manufacturing plant south of Richmond, Va., to a pair of Houston fundraisers. Framing the trip: a new monthly jobs report showing employers 227,000 jobs in February, the latest sign that the economy is headed in the right direction.

Every month’s jobs report is seen as a barometer of the economy and an important factor in the presidential race. The unemployment rate held steady at 8.3 percent, the result of more Americans looking for work as job growth takes hold month by month.

The jobs report and split loyalties among Republican voters assessing Mitt Romney, Rick Santorum and the rest of the GOP field give Obama’s team renewed confidence the path he has forged could help him win re-election and rebuild the economy. But privately, his advisers know that outside factors in the United States and abroad — from high gasoline prices to instability in the Middle East — could still derail his political and economic ambitions in the months leading to the fall election.

Pointing at Republicans, Obama said: “They think you have amnesia. They think you’ve forgotten how we got into this mess.”

He spoke at Union Station at Minute Maid Park, home of the Houston Astros, with tickets starting at $500 per person.

Defending his health care law, Obama said preventive care for women was now covered, including “checkups, mammograms, birth control. We fought for this because the top doctors and medical experts in the country said this kind of preventive care saves women’s lives,” he said, arguing too that it saves money.

Obama’s policy on access to contraception has faced criticism from Republicans and religious groups, who said the mandate that birth control be covered by insurance, even for employers whose faiths forbid contraception, was a violation of the Constitution’s guarantee of religious freedom.

“So when you see politicians who are trying to take us back to the days when this care was more expensive and harder to get for women — and I know you’re seeing some of that here in Texas — you just remember we can’t let them get away with it,” Obama said. “We fought for this change. We’re going to protect this change.”

Both in Houston and on the factory floor in Virginia, the president cautioned that too many Americans still long for work. But he said the nation’s economy had made progress because of difficult decisions he made, including rescuing U.S. automakers.

Romney, campaigning in Jackson, Miss., took a different view: The unemployment rate remains above 8 percent. “This president has not succeeded; this president has failed — and that’s the reason we’re going to get rid of him in 2012,” Romney said.

Obama was stocking up on campaign cash as Republicans appear locked in a primary process that may not be settled for months.

Republican Gov. Robert McDonnell of Virginia, who joined Obama at the factory and has been talked about as a potential vice presidential candidate, said he was heartened by Obama’s recognition of the innovative Virginia plant. “When the president is right, I’m going to commend him and say he’s doing things right,” he said.

“If he really wants to get Americans back to work, he needs to look at cutting the taxes and the bureaucracy and the regulatory burden on American business,” McDonnell said.

Yet every strong month of hiring undermines arguments from Republicans that Obama has failed to deliver on promises to pull the economy out of recession. Since the beginning of December, the country has added 734,000 jobs, the strongest three months of pure job growth since the Great Recession.

Obama has highlighted the U.S. economy’s addition of 429,000 manufacturing jobs during the past two years, touring factories in Wisconsin, Washington state and North Carolina in recent weeks. The United States lost 2.2 million manufacturing jobs in the two years before that.

Political calculations are not far from the surface in these trips — Virginia is expected to be a major election battleground later this year, and the Houston fundraisers added to the president’s campaign bankroll. Though the end of January, Obama’s campaign and the Democratic Party have raised about $250 million.

In Virginia, Obama promoted a $1 billion plan to create a network of up to 15 regional institutes to create partnerships among private industry, universities and community colleges and government. He also announced a $45 million pilot program that would show the type of potential collaboration among academia and industry.

In Texas, Obama was raising campaign cash among supporters who live in a reliably Republican state. Jimmy Carter, in 1976, was the last Democratic presidential candidate to carry Texas, but changing demographics and an influx in Hispanic voters have given Democrats hopes of competing in the state beyond the 2012 elections.